Fuzzy subfields of finite fields (Q1311733)

Basic structure theorems are given for fuzzy subfields of finite fields. In particular, the result that a finite field \(F\) is generated over its prime subfield \(\mathbb{Z}_ p\) by any generator of the multiplicative group \(F\setminus\{0\}\) is carried over to fuzzy subfields of \(F\). It is also shown that every subfield of \(F\) is a direct sum of fuzzy subgroups (whose supports are cyclic and of order \(p\)) of the additive group \(F\).